Open Channel Flow Calculator
Compute flow rate and velocity in open channels — rivers, ditches, and culverts — using Manning's equation. Use it for drainage design, irrigation channel sizing, and flood capacity analysis.
About this calculator
Manning's equation calculates the average flow velocity in an open channel: V = (1/n) × R_h^(2/3) × S^(1/2), where n is Manning's roughness coefficient (dimensionless), R_h is the hydraulic radius (cross-sectional area divided by wetted perimeter, in metres), and S is the channel slope (dimensionless, m/m). Volumetric flow rate is then Q = V × A, where A is the cross-sectional area. For a trapezoidal channel, A = (b + z × y) × y and wetted perimeter P = b + 2y√(1 + z²), giving R_h = A/P, where b is bottom width, y is water depth, and z is the side slope ratio (H:V). Manning's n typically ranges from 0.010 for smooth concrete to 0.035 for natural earthen channels. The equation is empirical, calibrated against field measurements, and is the standard tool in open-channel hydraulics for design and flood routing.
How to use
Design a trapezoidal concrete channel (n = 0.013) with bottom width b = 2 m, side slope z = 1.5, water depth y = 1 m, and slope S = 0.001. Area A = (2 + 1.5 × 1) × 1 = 3.5 m². Wetted perimeter P = 2 + 2 × 1 × √(1 + 1.5²) = 2 + 3.606 = 5.606 m. Hydraulic radius R_h = 3.5 / 5.606 = 0.624 m. Velocity V = (1/0.013) × 0.624^(2/3) × 0.001^(1/2) = 76.92 × 0.7357 × 0.03162 ≈ 1.79 m/s. Flow rate Q = 1.79 × 3.5 ≈ 6.27 m³/s. Enter your channel dimensions, slope, and material to get instant results.
Frequently asked questions
What is Manning's roughness coefficient and how do I choose the right value?
Manning's roughness coefficient (n) is an empirical value that quantifies the resistance of a channel surface to flow. Lower values indicate smoother surfaces: smooth concrete has n ≈ 0.012, while a natural river with weeds and irregular banks might have n ≈ 0.040–0.060. Selecting the correct n is critical because velocity is inversely proportional to n — doubling n halves the computed velocity. Published tables in references such as Chow's 'Open Channel Hydraulics' or USGS guidelines provide n values for dozens of channel types. When in doubt, use a slightly higher (more conservative) n value to avoid underestimating the required channel size.
How does channel slope affect flow rate in an open channel?
Channel slope S appears as S^(1/2) in Manning's equation, so flow velocity is proportional to the square root of the slope. Quadrupling the slope doubles the flow velocity and therefore doubles the flow rate for the same channel geometry and depth. Steeper slopes also increase flow velocity to the point where it can cause erosion of earthen channel beds, which is why designers specify maximum permissible velocities for different materials. Very shallow slopes risk insufficient self-cleaning velocity in drainage channels, allowing sediment to accumulate. Balancing slope selection against erosion and sediment transport is a key part of channel design.
What is hydraulic radius and why does it matter for open channel flow calculations?
Hydraulic radius (R_h) is the ratio of the channel's cross-sectional flow area to its wetted perimeter: R_h = A / P. It represents how efficiently the channel cross-section conveys flow relative to the frictional resistance of the wetted boundary. A large hydraulic radius means more flow area relative to the friction-producing perimeter, resulting in higher velocities for the same slope and roughness. Circular pipes flowing full have R_h = D/4. For a given cross-sectional area, a semicircular channel shape maximizes R_h and thus flow capacity, which is why sewer pipes are circular. Trapezoidal channels with optimum proportions approach this ideal for open-channel applications.